Computer Based Method of Pricing Equity Indexed Annuity Product with Guaranteed Lifetime Income Benefits

ABSTRACT

A computer-based method for determining a set of equity-indexed crediting parameters E for a lifetime-income equity-indexed deposit product provided to a set of owners having a set of dates of birth B, a rider charge C, a lifetime income percentage scale L, a set of profitability requirements R, a principal amount P, and an account value A. The method can include the steps of: establishing the values of C, L, R, P, A and E at a time when said deposit product is purchased; generating a set of yield curve and equity index scenarios consistent with valuation parameters; setting a trial value E i  for E; calculating the observed distribution D of profitability; comparing D with R; and, computing a revised trial value E i+1  for E, where the steps of establishing, generating, setting, calculating, comparing, and computing are performed by at least one general purpose computer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit, under 35 U.S.C. §119(e), of U.S.Provisional Application No. 60/790,194 filed Apr. 7, 2006, which ishereby incorporated by reference.

REFERENCE TO COMPUTER PROGRAM LISTING/TABLE APPENDIX

The present application includes a computer program listing appendix oncompact disc. Two duplicate compact discs are provided herewith. Eachcompact disc contains an ASCII text file of the computer program listingas follows:

File Name Size Created lir.log.txt 4600 KB 06/08/2006 1:17:51 PMlirval.log.txt 51 KB 06/08/2006 1:17:51 PM lirval1.txt 413 KB 06/08/20061:17:51 PM LMM1.DPR.txt 38 KB 06/08/2006 1:17:51 PM Rmem4p.dpr.txt 29 KB06/08/2006 1:17:52 PM SIMPLX.CPP 4 KB 06/08/2006 1:17:52 PMThe computer program listing appendix is hereby expressly incorporatedby reference in the present application.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for performingpricing and reserving calculations for an equity-indexed annuity thatprovides guaranteed lifetime income benefits in addition to providingadjustability in payment timing, access to the principal, and incomethat can increase as the stock index increases.

BACKGROUND OF THE INVENTION

Since their introduction in the mid-1990's, equity-indexed annuities(EIAs) have become very popular with annuity buyers. These productscombine security of principal with participation in equity indexreturns. They are therefore appealing to buyers who are risk-averse, butnonetheless want a chance to achieve the higher potential returnsassociated with equities. Recent sales statistics show EIAs making up40% or more of life insurance general-account annuity sales, comparedwith almost none a decade ago.

In order to provide EIAs on a profitable basis, a life insurance carriermust have an appropriate investment strategy and hedging system inplace. The potential for large losses if a carrier invests only inbonds, for example, but offers guaranteed returns based on stock-marketperformance is obvious. See, for example, U.S. Pat. No. 6,049,772 for adescription of the hedging activity and software required to support theissuing of EIAs.

Since the sharp decline in U.S. stock prices in early 2000, retailinvestors have developed a much greater appreciation of the risks ofdirect equity investment. As a result, they have been increasinglywilling to consider EIAs, because these are retirement savings vehiclesthat eliminate risks to principal while providing for equity-linkedreturns.

Similarly, as defined-benefit pension plan participation declines,retail investors are becoming increasingly aware of mortality risk: inthis case, the risk that a retiree may outlive his or her retirementassets. A defined benefit pension plan provides retirees with income forlife, and can reduce the associated mortality risk by means of“mortality pooling”. When mortality is pooled, the greater benefits thatmay be paid to a longer-lived retiree can to a large degree be offset bylesser benefits paid to a more short-lived retiree.

The continuing decline in defined-benefit pension plan participationmeans that retirees, if they restrict themselves to conventionalinvestments like stocks and bonds, are increasingly being forced toaccept mortality risk. They must therefore plan for the “worst case”(living to an advanced age) and budget accordingly.

However, mortality pooling can also be provided by life insurancecarriers. By making a guaranteed lifetime income available to annuitybuyers on a pooled basis, the need for any one buyer to invest for the“worst case” is eliminated, and so a higher level of income can beguaranteed for a given starting principal amount. Any one buyer'sprincipal need only provide for the “average case”, not the “worstcase”.

The guaranteed lifetime income benefit being described should not beconfused with annuitization, i.e. the purchase of a single-premiumimmediate annuity (SPIA). SPIA's are described in, e.g., Life Insurance(10th edition) by S. S. Heubner & Kenneth Black.

Although both the EIA guaranteed lifetime income benefit and SPIAs relyon mortality pooling, there are a number of critical differences. AnSPIA provides lifetime income, but does so on a basis that is extremelyinflexible. For example, SPIAs typically allow little opportunity forthe owner to access principal after income has started (althoughcommutation of a certain portion of payments may sometimes be negotiatedwith a carrier). This is in fact one of the most commonly-voicedobjections to the purchase of an SPIA: annuity buyers do not want toirrevocably surrender control of their principal to a life insurancecompany. Additionally, the vast majority of SPIAs do not provide for anincome that can increase over time depending on stock index performance:instead, the income amount is fixed at issue and cannot vary thereafter.Furthermore, SPIAs do not allow for flexibility in the timing ofpayments over the course of a year. Typically, the same amount is paidout each month, regardless of the cashflow requirements of the owner.

Life insurance carriers have recently started to add guaranteed lifetimeincome benefits to variable annuities (VA), but once again these aredistinct from the benefit described here. It is more difficult for alife insurance carrier to offer profitably with a VA, because they havemuch more basis risk, i.e., the risk that the financial instrumentsavailable for hedging will fail to match the behavior of the liability.

For example, many of the mutual funds offered in a typical VA areactively managed. This means that their performance will generally notmatch the performance of readily-available hedging instruments such asS&P 500 futures, for at least three reasons: 1) The asset mix held bythe mutual fund manager will have the same investment return as a quotedindex only by coincidence; 2) The mutual fund will have higher tradingcosts and expenses than would be typical of investment in, e.g., anunmanaged index through an exchange-traded fund; and 3) The fund managermay vary the allocation of assets between equities and fixed income inan attempt to outperform the market. Any such trading strategy willcreate additional optionality in the fund's values and make it harderfor the life insurance carrier to hedge. Additionally, the owner of thevariable annuity may transfer money from one fund to another or to afixed interest account at unpredictable intervals, magnifying the basisrisk problem.

Calculation of VA statutory reserves can be more complex andcomputation-intensive, at least given current regulatory requirements.VA reserves require calculation of a conditional tail expectation (CTE)of the greatest accumulated loss over a large number of scenarios andtherefore require detailed Monte Carlo simulation of both assets andliabilities.

The VA lifetime income benefit also has disadvantages from the point ofview of the buyer. A lifetime income benefit attached to a VA willtypically not provide any accumulation guarantees in addition to theincome benefit, so it may be harder to meet emergency cashflow orcritical illness expenses using such a product.

Thus, there is a long felt need for a method and apparatus forperforming pricing and reserving calculations for an equity-indexedannuity that does not restrict access to the principal, which allowsincome to increase with increases in the stock index, and which does nothave rigid payment windows.

SUMMARY

The invention broadly comprises a computer-based method for determininga set of equity-indexed crediting parameters E for a lifetime-incomeequity-indexed deposit product provided to a set of owners having a setof dates of birth B, a rider charge C, a lifetime income percentagescale L, a set of profitability requirements R, a principal amount P,and an account value A. The method can comprise the steps of:establishing the values of C, L, R, P, A and E at a time when thedeposit product is purchased; generating a set of yield curve and equityindex scenarios consistent with valuation parameters; setting a trialvalue E_(i) for E for the product; calculating the observed distributionD of profitability using the scenarios established; comparing D with R;and, computing a revised trial value E_(i+1) for E for the product. Thesteps of establishing, generating, setting, calculating, comparing, andcomputing are performed by at least one general purpose computerspecially programmed to perform the steps of establishing, generating,setting, calculating, comparing, and computing.

In some aspects, the method includes the step of calculating thelifetime income percentage scale L depending on an elapsed time betweenthe latest date from the set B and a time when income commences. Themethod can also include equity-index linked increases dependent on theelapsed time between the latest date in the set B and the date of eachincrease. The method can also include point-to-point equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a percentage of an increase in anequity index, credited at the end of each policy year. The credit can beno less than an annual minimum value and optionally no greater than anannual maximum value.

In some aspects, the method includes point-to-average equity indexcredits specified by the set of equity-indexed crediting parameters E,where the index credits are calculated using a percentage of an increasein an equity index from a year-start value to an average of values overthe policy year, and the credit is credited at the end of each policyyear. The credit can be no less than an annual minimum value andoptionally no greater than an annual maximum value.

In some aspects, the method includes point-to-point equity index creditsspecified by the set of equity-indexed crediting parameters E, where thecredits are calculated using a percentage of an increase in an equityindex, and the credit is credited at the end of an index interval equalto an integral number N of policy years. The credit can be no less thana minimum value and optionally no greater than a maximum valuecalculated during each index interval.

In some aspects, the computer-based method includes point-to-averageequity index credits specified by the set of equity-indexed creditingparameters E, where the credits are calculated using a percentage of anincrease in an equity index from a starting value to an average ofvalues over an index interval equal to an integral number N of policyyears, and the credit is credited at the end of the index interval. Thecredit can be no less than a minimum value and optionally no greaterthan a maximum value calculated during each index interval.

In some aspects, the computer-based method includes point-to-pointequity index credits specified by the set of equity-indexed creditingparameters E, where the credits are calculated using a weighted sum thatadds a compounded value calculated using a declared rate to a percentageof change in an equity index, and the credit is credited at the end ofan index interval equal to an integral number N of policy years. Thecredit can be no less than a minimum value and optionally no greaterthan a maximum value during each index interval.

In some aspects, the computer-based method includes point-to-averageequity index credits specified by the set of equity-indexed creditingparameters E, where the credits are calculated using a weighted sum thatadds a compounded value calculated using a declared rate to a percentageof change in an equity index from a starting value to an average ofvalues over an index interval equal to an integral number N of policyyears, and the credit is credited at the end of the index interval. Thecredit can be no less than a minimum value and optionally no greaterthan a maximum value during each index interval.

The invention also further broadly comprises a computer-based method fordetermining a set of equity-indexed crediting parameters E for alifetime-income equity-indexed deposit product provided to an ownerhaving a date of birth B, a rider charge C, a lifetime income percentagescale L, a set of profitability requirements R, a principal amount P,and an account value A. The method can include the steps of:establishing the values of C, L, R, P, A and E at a time when thedeposit product is purchased; generating a set of yield curve and equityindex scenarios consistent with valuation parameters; setting a trialvalue E_(i) for E for the product; calculating the observed distributionD of profitability using the index scenarios; comparing D with R;computing a revised trial value E_(i+1) for E for the product; and,calculating the lifetime percentage scale L depending on the elapsedtime between the date of birth B and a time when income commences. Thesteps of establishing, generating, setting, calculating, comparing,computing, and depending are performed by at least one general purposecomputer specially programmed to perform the steps of establishing,generating, setting, calculating, comparing, computing, and depending.The method can also include equity-index linked increases depending onthe elapsed time between date of birth B and a date when each increaseoccurs.

The invention also broadly comprises a computer-based apparatus fordetermining the value of a lifetime equity-indexed deposit product whichincludes a set of equity-indexed crediting parameters E for the lifetimeincome equity-indexed deposit product provided to a set of owners havinga set of dates of birth B, a rider charge C, a lifetime incomepercentage scale L, a set of profitability requirements R, a principalamount P, and an account value A, with C, R, L, P, A, and E determinedat a time when the deposit product is purchased. The seller is permittedto choose E and compute an observed distribution D of profitability ofthe deposit product such that D satisfies a set of profitabilityrequirements R.

In some aspects, the invention can include calculating the lifetimeincome percentage scale L depending on the elapsed time between a latestdate in the set B and a time when income commences or the date of eachincrease in income. The computer-based apparatus can also includepoint-to-point equity index credits specified by the set ofequity-indexed crediting parameters E, where the credits are calculatedusing a percentage of an increase in an equity index, and the creditscan be credited at the end of each policy year. The credit can be noless than an annual minimum value and optionally no greater than amaximum value.

In some aspects, the apparatus includes point-to-average equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a percentage of an increase in anequity index from a year-start value to an average of values over thepolicy year, and the credits are credited at the end of each policyyear. The credits can be no less than an annual minimum value andoptionally no greater than a maximum value.

In some aspects, the apparatus includes point-to-point equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a percentage of an increase in anequity index, and the credits are credited at the end of an indexinterval equal to an integral number N of policy years. The credit canbe no less than a minimum value and optionally no greater than a maximumvalue calculated during each index interval.

In some aspects, the apparatus includes point-to-average equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a percentage of an increase in anequity index from a starting value to an average of values over an indexinterval equal to an integral number N of policy years, and the creditsare credited at the end of the index interval. The credit can be no lessthan a minimum value and optionally no greater than a maximum valuecalculated during each index interval.

In some aspects, the apparatus includes point-to-point equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a weighted sum that adds acompounded value calculated using a declared rate to a percentage ofchange in an equity index, and the credit is credited at the end of anindex interval equal to an integral number N of policy years. The creditcan be no less than a minimum value and optionally no greater than amaximum value during each index interval.

In some aspects, the apparatus includes point-to-average equity indexcredits specified by the set of equity-indexed crediting parameters E,where the credits are calculated using a weighted sum that adds acompounded value calculated using a declared rate to a percentage ofchange in an equity index from a starting value to an average of valuesover an index interval equal to an integral number N of policy years,and the credit is credited at the end of the index interval. The creditcan be no less than a minimum value and optionally no greater than amaximum value during each index interval.

In some aspects, the invention further comprises a computer-basedapparatus for determining the value of a lifetime equity-indexed depositproduct which includes a set of equity-indexed crediting parameters Efor the lifetime income equity-indexed deposit product provided to anowner having a date of birth B, a rider charge C, a lifetime incomepercentage scale L, a set of profitability requirements R, a principalamount P, and an account value A. The values of C, R, L, P, A, and E canbe determined at a time when the deposit product is purchased, and aseller is permitted to choose E and compute an observed distribution Dof profitability of the product such that D satisfies a set ofprofitability requirements R. The lifetime income percentage L candepend on the elapsed time between at least one date of birth B and atime when income commences. The apparatus can also include equity-indexlinked increases depending on the elapsed time between date of birth Band a date when each increase occurs.

It is an object of the present invention to provide a computer basedmethod and apparatus for performing pricing and reserving calculationsfor an equity-indexed annuity that enables access to the principal ofthe annuity.

It is a another object of the present invention to provide a computerbased method and apparatus for calculating an equity indexed annuitythat can provide income that can increase over time depending on stockperformance.

It is a further object of the present invention to provide a computerbased method and apparatus for performing pricing and reservingcalculations for an equity indexed annuity that can provide flexibilityin the timing of income disbursements.

These and other objects and advantages of the present invention will bereadily appreciable from the following description of preferredembodiments of the invention and from the accompanying claims.

DETAILED DESCRIPTION OF THE INVENTION

While the present invention is described with respect to what ispresently considered to be the preferred embodiments, it is understoodthat the invention is not limited to the disclosed embodiments.

U.S. Provisional Application No. 60/790,194, filed Apr. 7, 2006, ishereby incorporated by reference in its entirety. This reference isincorporated herein by reference for the purpose of describing anddisclosing, for example, materials, systems, and methodologies that aredescribed in the references, which might be used in connection with thepresently described invention. The references discussed above andthroughout the text are provided solely for their disclosure prior tothe filing date of the present application. Nothing herein is to beconstrued as an admission that the inventors are not entitled toantedate such disclosure by virtue of prior invention.

The computer based method for performing pricing and reservingcalculations for an equity indexed annuity with guaranteed lifetimeincome benefit described herein addresses the problems found incurrently available retirement products in a way that provides annuitybuyers with additional flexibility. For example, the product does notrequire the buyer to irrevocably surrender control over their principal;income can increase over time depending on stock index performance; andthe owner has flexibility in the precise timing of income in each year.

Other problems associated with variable annuities (VA's), such as highertrading costs and expenses, variation in the allocation of assetsincrease difficulty in hedging, and higher basis risk, are not problemstypical of equity-indexed annuities (EIA's). Since performance of EIA'sis generally linked to an index that can be hedged using stock indexfutures, and reallocation between different indexing alternatives duringan indexing term is typically not permitted. This vastly simplifiesinvestment management for the product.

In contrast, EIA's, even with the lifetime guaranteed income benefit,can be valued using the Commissioners Annuity Reserve Valuation Method(CARVM) augmented with option valuation techniques in accordance withActuarial Guidelines 33 and 35. In many cases, dependent on theguarantee and surrender charge structure of the product, it may bepossible to establish that the statutory reserve is equal to theproduct's cash value, which will already be carried on the insurer'sadministrative system since it is needed for day-to-day administration.

Thus the EIA lifetime income benefit can be offered more easily on aprofitable basis, and has a number of operational advantages to the lifeinsurance carrier as well as being attractive from the point of view ofthe buyer.

Accordingly, there is a growing consumer need for an EIA that canprovide guaranteed lifetime income in addition to the well-knownaccumulation benefits and guarantees that EIAs typically provide. As adirect consequence, there is also a growing need among life insurancecarriers for a computer-based system that can determine reserves forsuch an EIA and price it so that it can be provided on a profitablebasis.

A Lifetime Income Rider (LIR) guarantees a minimum annual income for theowner during his or her lifetime. It does this by guaranteeing an annualwithdrawal amount that can be taken by the owner even if the AnnuityValue has been exhausted. The income amount is equal to a percentage ofthe highest Annuity Value on any anniversary once income has commenced.Although different designs can be constructed and priced using thesoftware by one skilled in the art, the following illustrative valuesprovide an example.

The earliest that income can commence is the owner's attained age 60.The income percentage if income begins before age 70 is 5%. For incomestarting at attained ages 70-79 it is 6%, and for income starting atattained ages of 80 and up it is 7%. The income amount is guaranteednever to decrease as long as the amount withdrawn per policy year doesnot exceed it, even if the Annuity Value falls to zero. The incomeamount is reduced in any year that the total withdrawal is greater thanthe income amount—the amount by which the withdrawal exceeds the incomeamount is called the overrun. The new income amount is then equal to:(a) the old income amount; multiplied by (b) the Annuity Value after theoverrun; and divided by (c) the Annuity Value before the overrun.

The income amount will increase if the Annuity Value is ever higher thanits level at the time of the first income payment. The annual premiumfor the LIR is currently 0.40% of the Annuity Value and is guaranteednot to exceed 0.75% for new issues. This rider guarantees that a clientcan receive an amount in each Policy Year up to the Income Amount, asdefined below, for that Policy Year, until the death of the Owner,regardless of the Annuity Value. If a client never takes a withdrawalgreater than the Income Amount in any Policy Year, the Income Amount isguaranteed never to decrease.

The Income Date is the date that income payments under this rider willbegin. The Income Date must be on or after the owner's 60th birthday (orif the Owner is not a natural person, the Annuitant's 60th birthday). Ifthe Income Date is not the Issue Date, the carrier must receive theowner's written request to establish the Income Date.

For each Policy Year, the Income Amount for that year is equal to theAdjusted Annuity Value at the start of that Policy Year times theLifetime Income Percentage, as shown on the data page. The LifetimeIncome Percentage depends on the age of the Youngest Owner (or the ageof the youngest Annuitant if the Owner is not a natural person) at theIncome Date.

This Rider guarantees that in each Policy Year after the Income Date,the client is entitled to receive an amount up to the Income Amount forthat year. The client is entitled to request to receive this amount inone to twelve payments even if the Annuity Value is zero. In any PolicyYear, the client may choose to withdraw less than the Income Amount forthat Year.

Provided the Annuity Value is greater than zero, these payments will bededucted from the Annuity Value but no Surrender Charges will apply tothese payments. The free withdrawal amount under the Policy will bereduced by the Income Amount. As with other Withdrawals, the carrierwill deduct the amount of the payment from the Annuity, and suchpayments will reduce the Annuity Value, the Surrender Value, and theDeath Benefit. In each Policy Year, if the client withdraws an amountgreater than the Income Amount it will be termed an Overrun. An Overrunwill generally reduce the Income Amount in future years.

On the Income Date, the Adjusted Annuity Value is equal to the AnnuityValue. After that date, the Adjusted Annuity Value is modified asfollows:

1. Each time an Overrun occurs, the Adjusted Annuity Value immediatelyprior to the Overrun is multiplied by an amount equal to (a) divided by(b) where,

(a)=The Annuity Value prior to the Overrun minus the Overrun

(b)=The Annuity Value prior to the Overrun.

2. On each Policy Anniversary, the Adjusted Annuity Value is set equalto the higher of its value at that time, or the Annuity Value on thatdate after all interest is credited and rider premiums are deducted.

Once declared, the Rider Annual Premium Rate cannot be changed. Whilethe rider is in force, the rider premium will be deducted from theAnnuity Value annually.

This rider terminates on the earliest of the following dates: Uponreceipt of the owner's written request to terminate this rider; When thePolicy terminates; When the client elects to start payments under asettlement option; When an Owner, who is a Natural Person, assigns theownership of the Policy; Upon death of the Owner or any Joint Owner; orWhen the Owner is not a Natural Person, and the Annuitant dies or a newAnnuitant is named.

Once the rider has been terminated, it may not be re-elected orreinstated. There will be no further premium due for this rider.However, the carrier will continue to deduct any outstanding riderpremiums until the earlier of the date that the Policy terminates, orwhen settlement option payments start.

As long as this rider is in force, even if the Annuity Value is zero,The client will continue to receive an amount up to the Income Amounteach Policy Year that the Owner (the youngest Owner on the Date of Issueif joint owners) is alive. If any income payments are made while theAnnuity Value is zero, other benefits under the Policy will beterminated, including the Death Benefit, the right to a distributionunder a settlement option, and the right to withdraw an amount largerthan the Income Amount.

The carrier must be notified of the death of the Owner on a timelybasis. If the carrier makes one or more payments under this rider afterthe death of the Owner, then the recipient must refund those paymentsplus interest at an annual rate of 6% or, if less, the maximum rateallowed by the state in which this Policy was sold.

At the Annuity Date, any income payments under this rider shall beprovided as a settlement option. If the client selects this settlementoption, then the Annuitant must be named as the Owner, and incomepayments will continue until the Death of the Owner. All other benefitsunder the Policy will terminate.

Programs are implemented in APL2000's APL*PLUS Windows Version 3.6,Borland's Delphi 4.0, and Borland C++. The APL language uses a specialcharacter set which includes a number of non-ASCII characters. We useJim Weigang's well-known reversible transliteration scheme to displayAPL source code using only ASCII characters. Because the transliterationscheme is reversible, standard utilities can be used to reconstruct theAPL source for execution by the APL interpreter. A preferred embodimentof the invention generates code in both a high-level interpretedlanguage (for ease of verification) and equivalent code in a compiledlanguage (for faster execution). Many different target languages couldplay these roles. In this implementation we use APL as the interpretedlanguage and Delphi (Borland Software's implementation of Object Pascal)as the compiled language, but many other language pairs (e.g.[Smalltalk,C++], or [Lisp, Fortran90]) are also possible. The assumedoperating system is Microsoft Windows (e.g. Windows 98 SE, Windows XP,or a similar operating system).

The pricing program calculates profitability for a model office (withassumed issue ages of 45, 55, 65, 73, 78, and 83) under a number ofdifferent utilization assumptions (“tracks”) for the lifetime incomebenefit. The lifetime income benefit is provided by the lifetime incomerider described above, and the tracks modeled are as follows: Track1—The EIA buyer does not add the lifetime income rider to the base EIApolicy, and so no rider premiums are charged and no lifetime incomebenefits are provided. Track 2—The EIA buyer adds the lifetime incomerider at issue and pays the rider charge from issue, but never actuallystarts taking the lifetime income benefit. This is primarily asensitivity test to determine what product profitability would be undersuch an assumption. One way that it could come about would be as aresult of a change in the buyer's financial resources or financial plan.For example, another financial asset held by the buyer could performvery well and generate enough income so that it does not becomenecessary to “dip into” the annuity value. Track 3—The lifetime incomerider is added at issue and the buyer starts taking lifetime income assoon as it is available—at age 60 for the younger issue ages (45 and 55)and immediately for the older issue ages (65, 73, 78, and 83). Track4—The lifetime income rider is added at issue and the buyer startstaking lifetime income five years after it is available—at age 65 forthe younger issue ages (45 and 55) and five years after issue for theolder issue ages (65, 73, 78, and 83).

The number of scenarios to be run for each issue age and utilizationassumption is currently set at 100. This parameter, along with manyothers, can be modified by editing the character matrixdelphi_rc_qual1_(—)7. The different parameters contained in this matrix,along with descriptions of the parameters, are included in the workspacelisting lir1.txt.

Other key assumptions are the rider premium rate (in this example, 0.40%of the annuity account value per year) and the lifetime income amount asa percentage of the annuity value (5% for attained ages at incomecommencement of 60-69, 6% for attained ages at income commencement of70-79, and 7% for attained ages at income commencement of 80 and up).

To determine expected profitability for the model office ofequity-indexed annuities including the lifetime income benefit, performthe following steps: Compile the dynamic link libraries (DLL's) in thedirectory where the APL interpreter (aplw.exe) resides. The source forlmm1.dll and rmem4p.dll is written in Delphi and the source forsimplex03.dll is written in C++; Start the APL2000 interpreter aplw.exe,and set working memory to approximately 256 Megabytes using the APLcommand) CLEAR 256000000; Load the pricing workspace LIR3; and, Type thename of the top-level function “main” and hit enter. The program willrun for approximately 6-8 hours on a 2.5 GHz Pentium computer, and iscomplete when the word “done” appears in the APL session log.

The program has a number of different reporting options for profitdistribution. The simplest is to examine the after-tax premium margin(ATPM) that is contained in the APL variable keepatpm.

Thus, the average statutory after-tax profit margin for each issue agewithin each track can be displayed by typing in the following APLexpression and hitting enter:

(6/1 2 3 4),(24{rho}45 55 65 73 78 83),[1.5]0.01{times}+/24 100 {rho}keepatpm, giving the following example result:

1 45 1.9416711 55 1.8628951 65 1.687711 73 1.3105851 78 1.5515721 83 1.5970962 45 3.1008382 55 3.0137992 65 2.8021382 73 2.3679422 78 2.542582 83 2.4892683 45 4.426953 55 3.7152893 65 2.7416773 73 1.8558073 78 2.1234913 83 1.9336134 45 4.5046394 55 4.1678424 65 3.5827324 73 2.8549874 78 2.8236354 83 2.745147

Similarly, a vector of statutory profits for each issue age/rider trackis stored in a variable called keepbookprofits once the program hasfinished running, and it can be displayed to show the year-by-year andscenario-by-scenario variations in profit results.

The program uses an approximation to the full-fledged CARVM-UMVstatutory reserve computation to achieve acceptable computational speed.This approximation has been validated by comparison with the results ofthe APL valuation workspace LIRVAL1.

Valuation Methodology for EIAs with Lifetime Income Benefit

The policy is an equity-indexed single-premium deferred annuity withannual credits based on a rate declared by the Company or on increasesin the S&P 500 Index. Three crediting methods are currently available:The Declared Rate Crediting Method, under which credits to the policyare based on an interest rate declared annually by the Company; The S&P500 Index One-Year Crediting Method, under which credits to the policyare based on annual point-to-point changes in the index, modified by aParticipation Rate (or percentage of participation), Cap (or maximumvalue), and Floor (or minimum value) declared annually by the Company;and the S&P 500 Index One-Year Averaged Crediting Method, under whichcredits to the policy are based on annual point-to-monthly-averagechanges in the index, modified by a Participation Rate, which is apercentage that the client participates, Cap, and Floor declaredannually by the Company.

The policy provides that a Premium Enhancement Amount, equal to aspecified percentage of premium, may be added by the Company to theAnnuity Value at the time of issue. The Premium Enhancement Amount willbe zero percent of the premium at launch, although it may be positivefor future new issues.

The policy includes a confinement and disability waiver of surrendercharges (Surrender Charge Waiver or SCW) provision that waives surrendercharges if the owner becomes disabled or is confined to a nursing home.This benefit is part of the base policy form rather than being madeavailable by rider or endorsement.

Three riders and endorsements providing additional benefits are alsoavailable: ROP—Return of Premium, which guarantees that the surrendervalue will not be less than the net premium for the annuity, adjustedfor withdrawals; LIR—The Lifetime Income Rider, which provides forannual lifetime income equal to a percentage of the highest AnnuityValue on any policy anniversary on or after the start of the income; andEEB—The Enhanced Earnings Benefit, which provides an additional deathbenefit equal to a percentage of the growth in the Annuity Value,adjusted for withdrawals.

The Lifetime Income Rider guarantees a minimum annual income for theowner during his or her lifetime. It does this by guaranteeing an annualwithdrawal amount that can be taken by the owner even if the AnnuityValue has been exhausted.

The income amount is equal to a percentage of the highest Annuity Valueon any anniversary once income has commenced. The earliest that incomecan commence is the owner's attained age 60. The income percentage ifincome begins before age 70 is 5%. For income starting at attained ages70-79 it is 6%, and for income starting at attained ages of 80 and up itis 7%.

The income amount is guaranteed never to decrease as long as the amountwithdrawn per policy year does not exceed it, even if the Annuity Valuefalls to zero. The income amount is reduced in any year that the totalwithdrawal is greater than the income amount. The new income amount isthen equal to: (a) the old income amount; multiplied by (b) the AnnuityValue after the excess withdrawal; and divided by (c) the Annuity Valuebefore the excess withdrawal.

The income amount will increase if the Annuity Value is ever higher thanits level at the time of the first income payment. The annual premiumfor the LIR is currently 0.40% of the Annuity Value and is guaranteednot to exceed 0.75% for new issues. The Earnings Enhancement Benefit(EEB) provides an additional benefit on death equal to a percentage ofthe growth in the Annuity Value, i.e., its excess over the singlepremium.

The percentage is equal to 45% for issue ages under 70, 25% for issueages 70-74, 20% for issue ages 75-79, and 15% for issue ages 80 to 85.The annual rider premium is currently 0.25% of the Annuity Value peryear and is guaranteed not to exceed 0.40% for new issues. The growth inthe Annuity Value is defined as the Annuity Value less the adjustedpremium.

At issue, the adjusted premium is equal to the premium. After anywithdrawal, the adjusted premium is equal to the adjusted premium on theprevious day multiplied by the Annuity Value after the withdrawal anddivided by the Annuity Value before the withdrawal.

Policy values for this policy form are the Annuity Value, the MinimumGuaranteed Surrender Value, and the Surrender Value. The Annuity Valueis the sum of the Crediting Method Account Values. If the policy is inforce at the Maturity Date then the greater of the Annuity Value and theMinimum Guaranteed Surrender Value will be applied to purchase animmediate annuity. A Premium Enhancement Amount, equal to a specifiedpercentage of premium, may be added by the Company to the Annuity Valueat the time of issue. The Premium Enhancement Amount will be zeropercent of the premium at launch, although it may be positive for futurenew issues. If positive, the Premium Enhancement Amount is allocatedpro-rata to each Crediting Method Account Value after the cancellationperiod and is eligible for surrender (subject to surrender charges), andalso for interest credits.

At launch, the available crediting methods for the policy will be theDeclared Rate Crediting Method, the S&P 500 Index One-Year CreditingMethod, and the S&P 500 Index One-Year Averaged Crediting Method.

The Declared Rate Crediting Method Account Value earns declared intereston a daily basis. A new interest rate is declared at the beginning ofeach policy year. Transfers can be made into or out of the Declared RateCrediting Method at each policy anniversary. The Declared Rate CreditingMethod Account Value is equal to the following: a) the net premium(single premium minus premium taxes) allocated to that account value,plus the pro-rata share of any Premium Enhancement Amount; plus b) Fixeddaily interest; plus c) Transfers into the account value on any policyanniversary; minus d) Transfers out of the account value on any policyanniversary; minus e) Any rider premiums deducted from the account;minus f) Any amounts surrendered from the account (including anyapplicable surrender charges).

At launch, the available equity-indexed crediting methods will be theS&P 500 Index One-Year Crediting Method and the S&P 500 Index One-YearAveraged Crediting Method. After launch, new equity-indexed creditingmethods may be added to the policy form by endorsement.

Indexed interest is credited at the end of each policy year. The amountto be credited equals the Account Value times the growth in the S&P 500Index over the policy year, but no less than the Account Value times theFloor, and no greater than the Account Value times the Cap. The Floor iscurrently 0% for both equity-indexed crediting methods.

For the S&P 500 Index One-Year Crediting Method, growth is measured bycomparing the starting value of the index with its ending value; for theS&P 500 Index One-Year Averaged Crediting Method, growth is measured bycomparing the average of its ending values on each policy month duringthe policy year with the starting value of the index.

Each Equity-Indexed Crediting Method Account Value is equal to thefollowing: a) The net premium (single premium minus premium taxes)allocated to that account value, plus the pro-rata share of any PremiumEnhancement Amount; plus b) Indexed interest on each policy anniversary;plus c) Transfers into the account value on any policy anniversary;minus d) Transfers out of the account value on any policy anniversary;minus e) Any rider premiums deducted from the account; minus f) Anyamounts surrendered from the account (including any applicable surrendercharges).

The Surrender Value of the policy is the greater of: the Annuity Value,less any surrender charge, and the Minimum Guaranteed Surrender Value.

The surrender charge schedule for the 7-year version of the policy formwill be as follows:

Years Surrender Charge as % completed of Annuity Value 0 7% 1 7% 2 6% 35% 4 4% 5 3% 6 2% 7 0%

The surrender charge schedule for the 10-year version of the policy formwill be as follows:

Years Surrender Charge as % completed of Annuity Value 0 9% 1 9% 2 8% 37% 4 6% 5 5% 6 4% 7 3% 8 2% 9 1% 10+ 0%The surrender charge is waived on the first 10% of the Annuity Value asof the beginning of each year in each policy year after the first.

Minimum Guaranteed Surrender Value—The Minimum Guaranteed SurrenderValue for the policy equals: a) the single premium paid by the owner(adjusted for premium taxes) multiplied by the Net ConsiderationPercentage; plus b) any Excess Interest Credits; less c) any amountssurrendered (not including any applicable surrender charge); less d) anyrider charges, e) all accumulated at the minimum guaranteed interestrate. The Net Consideration Percentage will be 90%.

The minimum guaranteed interest rate will be set at issue. It will atleast be equal to: the monthly average five-year Constant MaturityTreasury Rate as published by the Board of Governors of the FederalReserve Board for the second full calendar month preceding the issuedate, rounded to the nearest 0.05%, and reduced by 1.25%. For minimumguaranteed cash values linked to equity indexed crediting method accountvalues, the minimum guaranteed interest rate will be reduced by afurther R % to reflect equity participation (where R is between 0% and1%) provided, however, that such resulting rate will be no greater than3% nor less than 1%.

Indexed Interest Example—Assume the client takes no withdrawals prior tothe end of the policy year.

Assume the following:

The single premium is $10,000.

The Premium Enhancement Amount is $0.

The entire premium is allocated to the S&P 500 Index One-Year CreditingMethod.

No withdrawals are taken during the first policy year.

The Participation Rate is 100%.

The Cap Rate is 6.5%.

The Floor Rate is 0%.

The S&P 500 Index is 1,000 at issue.

The S&P 500 Index is 1,100 at the first policy anniversary.

Then the Equity Index Percentage Change is (1,100−1,000)/1,000, or 10%.Since this is greater than the cap of 6.5%, the interest credit is equalto $10,000×6.5%, which equals $650. This amount is added to the AccountValue, which is then $10,650.

The Death Benefit payable upon receipt of due Proof of Death will be thegreater of the Minimum Guaranteed Surrender Value and the Annuity Value.Indexed interest is credited on any equity-indexed crediting methods bytreating the date of death as the end of the equity-indexing year.

Valuation of the annuity during the deferral phase is in accordance withthe Commissioners Annuity Reserve Valuation Method (CARVM) under theStandard Valuation Law (SVL), as interpreted and clarified by ActuarialGuideline 33 (Determining CARVM Reserves for Annuity Contracts withElective Benefits) and Actuarial Guideline 35 (The Application of theCommissioners Annuity Reserve Method to Equity Indexed Annuities).

The company will value the annuity on an issue-year basis. Thecomputational method used will be the Commissioners Annuity ReserveMethod with Updated Market Values (CARVM-UMV). The plan, together withits riders, is a Type C annuity as defined in the SVL. There is nomarket-value adjustment (MVA) to withdrawn values, i.e. funds can bewithdrawn in installments over less than five years without adjustmentto reflect changes in interest rates or asset values since receipt ofthe funds by the insurance company. No guarantee is extended forcredited interest rates on annuity considerations received more than oneyear from the date of issue, since the plan is a single-premiumcontract.

In order to apply Actuarial Guideline 33, each of the benefits offeredby the policy must be classified as elective or non-elective forpurposes of development of integrated benefit streams. Briefly, thebenefits can be classified as: Elective: The elective benefits offeredby the policy are surrender, annuitization, and the LIR benefit.Non-elective: The non-elective benefits offered by the policy are thepolicy death benefit, the EEB, and the Surrender Charge Waiver. Sincethey are non-elective it is appropriate to use incidence rates for thesebenefits in the development of integrated benefit streams. As describedin Parts 3 & 4 of the text of Actuarial Guideline 33, valuation interestrates are determined using contract-level and benefit-level parameters,and generally will vary depending on whether benefits are elective ornon-elective.

Surrender and withdrawal benefits provided by the plan and its ridersare elective benefits and are valued using the Type C valuation interestrate. The Declared Rate, Participation Rate, Floor, and Cap for theannuity are declared annually, and so a guaranteed duration of one yearis used.

Death benefits under the plan and its riders, being non-electivebenefits, are discounted using the Type A valuation rate with aguarantee duration of one year as prescribed by Section 4(C) of the textof Actuarial Guideline 33. Similarly, the benefit provided by theSurrender Charge Waiver is also a non-elective benefit and it is alsovalued using the Type A valuation interest rate with a guaranteeduration of one year.

Annuitization benefits are available for life (optionally with aguarantee period of ten or twenty years) or as installments over fiveyears or more. They are valued using the Type A valuation rate with aguarantee duration equal to the number of years after issue thatannuitization is assumed to occur, as prescribed in Section 4(B) of thetext of Actuarial Guideline 33.

Actuarial Guideline 35 prescribes four computational methods forequity-indexed annuities that may be considered to be acceptableinterpretations of CARVM. These are the Enhanced Discounted IntrinsicMethod (EDIM), the Commissioners Annuity Reserve Valuation Method withUpdated Market Values method (CARVM-UMV), the Market Value ReserveMethod (MVRM), and the Black-Scholes Projection Method (BSPM), a variantof the MVRM.

According to Actuarial Guideline 35, General Requirements on the Use ofCertain Computational Methods, the policy form design must feature asingle dominant benefit in order for the EDIM, MVRM, and BSPMcomputational methods to be considered to be acceptable interpretationsof CARVM. The single dominant benefit is the most likely benefit to beprovided under the policy form according to criteria defined in theGuideline.

The benefits provided by the Enhanced Earnings Benefit Rider (EEB) andLifetime Income Rider (LIR) are not concentrated at a single duration.The benefits provided by the LIR depend on the date at which incomecommences: this date is selected by the owner after issue and is notknown to the Company in advance.

Additionally, a policy may be issued with both EEB and LIR. In this casethe relative magnitudes of the benefits under EEB (which becomes morevaluable if mortality increases) and LIR (which becomes more valuable ifmortality decreases) are not known at issue. Therefore, depending on theriders that have been chosen, it may be the case that this form does notmeet the Guideline's requirements for the use of EDIM, MVRM, and BSPM.Accordingly, the valuation will be performed using the CARVM-UMVcomputational method, as being uniformly applicable to all cases.

As outlined in Actuarial Guideline 35's Description of ComputationalMethods (Attachment I to the Guideline), in order to perform a CARVM-UMVvaluation, policy benefits must be resolved into two components: theguaranteed floor benefits at each duration; and any benefit that canarise at each duration in excess of the guaranteed floor benefits. Anysuch excess is defined as an equity-indexed benefit, and the marketvalue of an index option having this benefit as payoff is then used inthe CARVM-UMV calculation.

The Guideline requires that these option market values be accumulated atthe valuation interest rate to the option expiry date and added to theguaranteed floor benefits. The option market values for the differentbenefit streams will in general be accumulated at different rates,because Actuarial Guideline 33 requires the application of differentvaluation interest rates for elective and non-elective benefits, anddifferent valuation interest rates for surrenders and annuitizations.

Guaranteed minimum floor benefits and option values are thereforedeveloped for each of the following benefit streams: Death benefits(including benefits under the EEB rider, if this rider has been added);Annuitization benefits; Surrender charge waiver benefits; Surrender andpartial withdrawal benefits; and, LIR (guaranteed lifetime income)benefits.

Once these guaranteed minimum floor benefits and option values have beencomputed, the option market values can be accumulated at the applicablevaluation interest rates to the option expiry dates and added to theguaranteed floor benefits. A CARVM valuation of the resulting totalbenefit streams is then performed.

The determination of guaranteed floor benefits for the policy isstraightforward if no riders are attached. Minimum policy values (andhence guaranteed floor benefits) can be calculated by assuming that 100%of premium is allocated to the equity-indexed crediting methods and thatthere is no growth in the S&P 500 Index, i.e., by assuming a scenario inwhich the year-on-year growth in the index is zero or negative.

In this no-growth case, the Annuity Value stays constant until thedeferral period ends (by death, surrender, or annuitization), and theMinimum Guaranteed Surrender Value grows at the minimum guaranteedinterest rate until the deferral period ends.

Adding the EEB rider and the LIR makes determination of guaranteed floorbenefits more complex. The policy form provides that EEB and LIRpremiums will only be deducted from the Annuity Value (and reflected inthe Minimum Guaranteed Surrender Value calculation) to the extent thatthere is sufficient indexed interest to pay for them. In other words,the form provides that rider premiums will never force the Annuity Valuebelow its initial level in the absence of other withdrawals.

Any excess rider premiums are carried forward and deducted to the extentpossible when either a) the policy is surrendered or b) additionalindexed interest is credited. We refer to this as “rider chargecarryforward”. This treatment of rider premiums implies that theno-growth scenario may not generate the minimum possible policy values.They may actually be lower in a “low growth” scenario, in which theindexed interest is just sufficient to pay for rider charges each year,or in a “sporadic growth” scenario, where the index stays constant for10 years and then jumps by 10%. This result occurs because in theno-growth scenario, rider premiums are never deducted from the MinimumGuaranteed Surrender Value. In contrast, in the sporadic growthscenario, there is eventually enough growth in the Annuity Value toallow rider premiums to be deducted, and the corresponding minimumguarantee calculation drives the Minimum Guaranteed Surrender Valuelower than it would have been in the no-growth case.

Calculation of market values for benefit options is straightforward inthe case where the base policy is stand-alone, but becomes more complexwhen the EEB rider and the LIR are added. There are two main reasons forthis: First, the income for the LIR is based on the highest anniversaryAccount Value since income commencement. This benefit resembles a“discrete lookback” or “highwater mark” option, for which there are nouseful closed-form solutions: a numerical approximation method must beused instead. Secondly, the Rider charge carryforward complicates thedetermination of the guaranteed floor benefits, as described above.Since the benefit options in CARVM-UMV are by definition any excessesover the guaranteed floor benefits, rider charge carryforward naturallyalso complicates the determination of the benefit option values.

Monte Carlo simulation often provides the simplest approach to optionvaluation in the absence of closed-form solutions, and that turns out tobe true here. We generate stochastic stock index scenarios from arisk-neutral distribution and use them to drive simulated policy valuecalculations. Using a Monte Carlo approach makes it relatively simple toincorporate rider charge carryforward into the guaranteed floor benefitcalculation. “No growth” and “low growth” scenarios are generated inaddition to the stochastic stock index scenarios (we refer to the entireset of scenarios as the “augmented scenarios”), and the guaranteed floorbenefits are determined as the minimum benefits over the augmentedscenarios.

The benefit option payoffs are then the average of the excesses of thestochastic scenario benefits over the guaranteed floor benefits. Theseoption payoffs, discounted to the valuation date using the risk-neutralinterest rate, provide the option market values required by CARVM-UMV.The option market values are accumulated to the option expiry dates atthe appropriate valuation interest rates and added to the guaranteedfloor benefits to yield the total benefits required for a CARVMvaluation.

Assumptions for CARVM-UMV Valuation Examples—Mortality in the examplesis assumed to follow the a2000 table. Incidence rates for valuation ofthe disability benefit are taken from Exhibit 2 of the Report of theCommittee to Recommend New Disability Tables for Valuation (Transactionsof the Society of Actuaries, Vol. XXXVII). Class 2 incidence rates foraccident and sickness are used. Note that the policy form firstestablishes that a claim for Social Security Disability benefits hasbeen approved before surrender charges will be waived. Under reasonableassumptions with respect to approval times (4 months) andreconsideration times (4 months) for Social Security Disability claims,this is equivalent to requiring an elimination period of 90 days. Anelimination period of 90 days is used because this is the longestelimination period contained in the table.

Incidence rates for valuation of the nursing home benefit are taken fromTable D-3 of the Long-Term-Care Intercompany Study: 1984-1991 Experience(Transactions, Society of Actuaries, 1993-94 Reports). In accordancewith the policy form provisions, an elimination period of 60 days isassumed. Because the study does not break out data for the 60 dayelimination period, incidence rates for elimination periods of 15-30days are used as a conservative approximation.

Type A and Type C valuation interest rates for the example arecalculated using the formula in the Section 4(B) of the StandardValuation Law and the weighting factors specified, assuming a referenceinterest rate R of 5.5%. The resulting valuation rates are:

Guarantee Duration Type A Type C (Years) Rate Rate   ≦5 5.25% 4.50%  >5,≦10 5.00% 4.50% >10, ≦20 4.75% 4.25% >20 4.25% 4.00%The actual valuation rates used will depend on the actual value of thereference interest rate R for each year of issue.

Point-to-point equity-indexed crediting was assumed for the examples,with a participation rate of 100%, a floor of 0%, and a cap varying bypolicy year. The assumed cap was 6.5% in the first policy year, 4% inpolicy years 2-7, and 2% thereafter.

The assumed guaranteed interest rate for calculation of the MinimumGuaranteed Surrender Value in the examples is 1.85%. The actualguaranteed interest rates for policies will vary according to the actualvalue of the monthly average five-year Constant Maturity Treasury Rate,as specified supra regarding Policy Values, i.e., Annuity Value, MinimumGuaranteed Surrender Value, and Surrender Value.

The stochastic stock index scenarios were generated using a log normaldistribution (Black-Scholes assumptions) with an assumed risk-freeinterest rate of 5% continuously compounded and a dividend yield of 2%.The number of stock index scenarios generated was 100,000.

CARVM-UMV Valuation Examples—The surrender charge waiver benefit iscontained in the base contract and so this benefit is included in eachexample. Therefore, the examples cover the base contract with or withoutthe (independently selectable) Return of Premium, Enhanced EarningsBenefit, and Lifetime Income Rider (with three assumed income startdates for the LIR).

This gives us sixteen examples in total for a given free partialwithdrawal schedule. Because free partial withdrawals affect both basepolicy benefits and rider benefits, we show reserve values assuming fullutilization of free partial withdrawals and showing no utilization—thehigher of the two is the CARVM reserve that would actually be held.

All example calculations assume a seven-year surrender chargescale—calculations for the ten-year surrender charge scale areanalogous. Similarly, the examples all assume crediting based on thepoint-to-point crediting method—calculations for the point-to-averagecrediting method are analogous.

The calculations all show the derivation of the reserve at issue for a$10,000 policy issued to a male aged 55.

The column headings in the examples shown in lirval1.txt have thefollowing meanings t—the number of years since the issue date; mindb—theminimum death benefit realized over the augmented scenarios; dbproj—themarket value of the death benefit option at the valuation date,projected forward at the valuation interest rate; minfpw—the minimumfree partial withdrawal benefit realized over the augmented scenarios;fpwproj—the market value of the free partial withdrawal benefit optionat the valuation date, projected forward at the valuation interest rate;minns—the minimum net surrender benefit (cash value less any outstandingrider premiums) realized over the augmented scenarios; nsproj—the marketvalue of the net surrender benefit option at the valuation date,projected forward at the valuation interest rate; mindiss—the minimumdisability/nursing home benefit realized over the augmented scenarios;dissproj—the market value of the disability/nursing home benefit optionat the valuation date, projected forward at the valuation interest rate;minann—the minimum annuitization benefit realized over the augmentedscenarios, assuming annuitization to a ten-year certain period annuity;annproj—the market value of annuitization benefit option at thevaluation date, projected forward at the valuation interest rate;tpx—the proportion of initial lives still in force per unit issued;t|qx—the mortality decrement per unit issued; t|dx—the disability andnursing home decrement per unit issued; vta—the discount factor for theType A valuation interest rate for each guarantee duration; pvdb—thepresent value of death benefits through time t at the Type A valuationrate; pvdiss—the present value of disability/nursing home benefitsthrough time t at the Type A valuation rate; vtc—the discount factor attime t of the Type C valuation interest rate a guarantee duration of oneyear; pvfpw—the present value of the free partial withdrawal benefitusing the Type C valuation interest rate; pv(s,an)—the maximum of i) thepresent value of the annuitization benefit using the Type A valuationinterest rate and ii) the present value of the net surrender benefitusing the Type C valuation interest rate; and, sumpv—the sum of thepresent values of the benefits for each duration. As can be seen fromthe examples, the reserve at issue reduces to the cash value of thepolicy (in the absence of the ROP benefit) or to the premium (with ROP).

The minimum annuity payments under the contract are based on the a2000Individual Annuity Valuation Tables, sex-distinct, with interest at 1.5%per year, which are Basis of Settlement Option Factors. The attained ageat annuitization will be adjusted downward by one year for each fullfive year period that has elapsed since Jan. 1, 2000.

The valuation of annuity payments for policies that have annuitized willuse the valuation mortality table applicable for the calendar year ofcontract issue and the appropriate

SPIA valuation interest rate applicable for the calendar year ofannuitization.

Method of Operation of the Valuation Program. Type testcases and hitenter. Results of CARVM-UMV reserve calculation appear in APL session.

In a preferred embodiment, the method of the invention is implemented bya specially programmed general purpose computer. The steps of the methodare implemented by an arithmetic logic unit of the computer with datastored in short term (RAM) and long term memory. In the apparatus claimsthe functional language is intended to comprise the arithmetic logicunit of the computer together with memory.

As indicated above, the present invention can be embodied in the form ofan apparatus with means for the implementing the method,computer-implemented processes and apparatuses for practicing thoseprocesses. The present invention can also be embodied in the form ofcomputer program code embodied in tangible media, such as floppydiskettes, CD-ROMs, DVDs, hard drives, or any other computer-readablestorage medium, wherein, when the computer program code is loaded intoand executed by a computer, the computer becomes an apparatus forpracticing the invention. The present invention can also be embodied inthe form of computer program code, for example, whether stored in astorage medium, loaded into and/or executed by a computer, ortransmitted as a propagated computer data or other signal over sometransmission or propagation medium, such as over electrical wiring orcabling, through fiber optics, or via electromagnetic radiation, orotherwise embodied in a carrier wave, wherein, when the computer programcode is loaded into and executed by a computer, the computer becomes anapparatus for practicing the invention. When implemented on a futuregeneral-purpose microprocessor sufficient to carry out the presentinvention, the computer program code segments configure themicroprocessor to create specific logic circuits to carry out thedesired process.

Thus it is seen that the objects of the invention are efficientlyobtained, although modifications and changes to the invention should bereadily obvious to those having ordinary skill in the art, and thesemodifications are intended to be within the scope of the claims.

1-34. (canceled)
 35. A computer-based method for determining a set ofequity-indexed crediting parameters for a lifetime-income equity-indexedproduct, comprising the steps of: establishing initial account values;generating a set of yield curves and equity index scenarios consistentwith a set of valuation parameters; setting a first trial value for saidset of equity-indexed crediting parameters for said product; calculatingthe observed distribution of profitability using said scenarios;comparing the observed distribution of profitability using saidscenarios with the set of profitability requirements; and computing arevised trial value for said set of equity-indexed crediting parametersfor said product.
 36. The computer-based method as recited in claim 35,further comprising the step of calculating a lifetime income percentagescale depending on an elapsed time between a birthdate of the owner orowners and a time when income commences.
 37. The computer-based methodrecited in claim 35, further comprising equity-index linked increasesdependent on the elapsed time between a birthdate of the owner or ownersand a date of each increase.
 38. The computer-based method recited inclaim 35, further comprising point-to-point equity index creditsspecified by said set of equity-indexed crediting parameters, whereinsaid credits are calculated using a percentage of an increase in anequity index, credited at the end of each policy year, and said creditis no less than an annual minimum value.
 39. The computer-based methodrecited in claim 35, further comprising point-to-point equity indexcredits specified by said set of equity-indexed crediting parameters,wherein said credits are calculated using a percentage of an increase inan equity index, credited at the end of each policy year, and saidcredit is no less than an annual minimum value, and said credit is nogreater than an annual maximum value.
 40. A computerized method foradministering an equity indexed annuity benefit plan offering at leastone owner of said plan a guaranteed lifetime income benefit, comprisingthe steps of: storing data relating to an equity indexed annuityaccount; receiving a request from said at least one owner for payment ofsaid guaranteed lifetime income benefit; determining whether said atleast one owner previously requested payment of said guaranteed lifetimeincome benefit; if said at least one owner had not previously requestedpayment of said guaranteed lifetime income benefit, then determining afirst Annuity Value, calculating a first income percentage, andcalculating a first income amount based in part on said first incomepercentage and said first Annuity Value and defining the guaranteedlifetime income amount as said first income amount; and annuallythereafter, determining a second Annuity Value, calculating a secondincome percentage, and calculating a second income amount based in parton said second income percentage and said second Annuity Value,comparing said first income amount to said second income amount anddetermining if said first income amount is greater than said secondincome amount, and redefining the guaranteed lifetime income amount asthe greater of said first income amount or said second income amount.41. A computerized method for administering an equity indexed annuitybenefit plan offering a guaranteed lifetime income benefit, comprisingthe steps of: storing data relating to an equity indexed annuityaccount; receiving a request for payment of said guaranteed lifetimeincome benefit; calculating a first lifetime income payment amount;determining whether a payment of said first lifetime income paymentamount was previously requested; if payment of said first lifetimeincome payment was previously requested and said payment was made,calculating a first Annuity Value on a date that said first incomepayment amount was paid; calculating a second income payment amount,comparing said first income payment to said second income payment amountand determining if said first income payment is greater than said secondincome payment amount; and defining the guaranteed lifetime incomeamount as the greater of said first income payment amount or said secondincome payment amount.
 42. The method of claim 41 further comprising thestep of providing a plurality of payment options for payment of saidguaranteed lifetime income amount.
 43. The method of claim 41 furthercomprising the step of determining an age of an owner of said planbefore said owner may be offered said guaranteed lifetime incomebenefit.
 44. The method of claim 41 further comprising the steps ofdetermining a revised Annuity Value if a previous income payment was notrequested; calculating an income percentage; calculating an incomeamount based in part on said income percentage and said calculatedrevised Annuity Value; and defining said calculated income amount as aguaranteed lifetime income amount.
 45. The method of claim 41 wherein anowner of said plan comprises an annuitant.
 46. The method of claim 41wherein said guaranteed lifetime income amount is paid in the form of aplurality of payments over a one year period.
 47. The method of claim 41wherein said income amount is equal to a percentage of a highest AnnuityValue on any contract anniversary once payment of income has beenrequested.
 48. The method of claim 41 wherein said equity indexedproduct comprises a life insurance product.